We report the discovery of 14 quasars in the vicinity of HE 2347−4342, one of the two quasars whose intergalactic He ii forest has been resolved with FUSE. By analysing the H i and the He ii opacity variations separately, no transverse proximity effect is detected near three foreground quasars of HE 2347−4342: QSO J23503−4328 (z = 2.282, ϑ = 3. 59), QSO J23500−4319 (z = 2.302, ϑ = 8. 77) and QSO J23495−4338 (z = 2.690, ϑ = 16. 28). This is primarily due to line contamination and overdensities probably created by large-scale structure. By comparing the H i absorption and the corresponding He ii absorption, we estimated the fluctuating spectral shape of the extragalactic UV radiation field along this line of sight. We find that the UV spectral shape near HE 2347−4342 and in the projected vicinity of the three foreground quasars is statistically harder than expected from UV background models dominated by quasars. In addition, we find three highly ionised metal line systems near the quasars. However, they do not yield further constraints on the shape of the ionising field. We conclude that the foreground quasars show a transverse proximity effect that is detectable as a local hardening of the UV radiation field, although the evidence is strongest for QSO J23495−4338. Thus, the relative spectral hardness traces the proximity effect also in overdense regions prohibiting the traditional detection in the H i forest. Furthermore, we emphasise that softening of quasar radiation by radiative transfer in the intergalactic medium is important to understand the observed spectral shape variations. From the transverse proximity effect of QSO J23495−4338 we obtain a lower limit on the quasar lifetime of ∼25 Myr.